Abstract

Let [Special characters omitted.] be a family of piecewise linear maps f : [-1,1] [arrow right] [-1,1] with a discontinuity at x = 0 such that f is expanding in one of the intervals (-1,0), (0,1) and contracting in the other. We will study the dynamics of maps of sub-classes of [Special characters omitted.] . It will be shown that a map in such a sub-class of [Special characters omitted.] either has a periodic attractor or is eventually expanding. In the latter case, there exists an absolutely continuous invariant measure (acim) and in many examples we will find the measure.